A kagome lattice originally referred to an arrangement of laths composed of interlaced triangles such that each point where two laths cross has four neighboring points, forming the pattern of a trihexagonal tiling. The name derives from the Japanese word kagome (籠目), a traditional woven bamboo pattern, composed from the words kago, meaning "basket", and me, literally meaning "eye(s)", referring to the pattern of holes in a woven basket. Although called a lattice, its crossing points do not form a mathematical lattice.
Some minerals, namely jarosites and herbertsmithite, contain layers with kagome lattice arrangement of atoms in their crystal structure. These minerals display novel physical properties connected with geometrically frustrated magnetism. The term is much in use nowadays in the scientific literature, especially by theorists studying the magnetic properties of a theoretical kagome lattice in two or three dimensions. The term "kagome lattice" in this context was coined by Japanese physicist Kōji Fushimi, who was working with Ichirō Shōji. The first paper on the subject appeared in 1951.
Read more about this topic: Trihexagonal Tiling